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Thu, 11 Oct 2007 11:20:18 +0200Thu, 11 Oct 2007 11:20:18 +0200The difference of the solutions of the elastic and elastoplastic boundary value problem and an approach to multiaxial stress-strain correction
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1900
In the theoretical part of this thesis, the difference of the solutions of the elastic and the elastoplastic boundary value problem is analysed, both for linear kinematic and combined linear kinematic and isotropic hardening material. We consider both models in their quasistatic, rate-independent formulation with linearised geometry. The main result of the thesis is, that the differences of the physical obervables (the stresses, strains and displacements) can be expressed as composition of some linear operators and play operators with respect to the exterior forces. Explicit homotopies between both solutions are presented. The main analytical devices are Lipschitz estimates for the stop and the play operator. We present some generalisations of the standard estimates. They allow different input functions, different initial memories and different scalar products. Thereby, the underlying time involving function spaces are the Sobolov spaces of first order with arbitrary integrability exponent between one and infinity. The main results can easily be generalised for the class of continuous functions with bounded total variation. In the practical part of this work, a method to correct the elastic stress tensor over a long time interval at some chosen points of the body is presented and analysed. In contrast to widespread uniaxial corrections (Neuber or ESED), our method takes multiaxiality phenomena like cyclic hardening/softening, ratchetting and non-masing behaviour into account using Jiang's model of elastoplasticity. It can be easily adapted to other constitutive elastoplastic material laws. The theory for our correction model is developped for linear kinematic hardening material, for which error estimated are derived. Our numerical algorithm is very fast and designed for the case that the elastic stress is piecewise linear. The results for the stresses can be significantly improved with Seeger's empirical strain constraint. For the improved model, a simple predictor-correcor algorithm for smooth input loading is established.Holger Langdoctoralthesishttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1900Thu, 11 Oct 2007 11:20:18 +0200A piecewise analytical solution for Jiangs model of elastoplasticity
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1898
In this article, we present an analytic solution for Jiang's constitutive model of elastoplasticity. It is considered in its stress controlled form for proportional stress loading under the assumptions that the one-to-one coupling of the yield surface radius and the memory surface radius is switched off, that the transient hardening is neglected and that the ratchetting exponents are constant.Holger Lang; Klaus Dressler; Rene Pinnaureporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1898Tue, 02 Oct 2007 12:27:59 +0200Lipschitz estimates for the stop and the play operator
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1773
In this article, we give some generalisations of existing Lipschitz estimates for the stop and the play operator with respect to an arbitrary convex and closed characteristic a separable Hilbert space. We are especially concerned with the dependency of their outputs with respect to different scalar products.Holger Lang; Klaus Dressler; Rene Pinnaureporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1773Thu, 21 Sep 2006 12:05:33 +0200Parameter optimization for a stress-strain correction scheme
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1702
A gradient based algorithm for parameter identification (least-squares) is applied to a multiaxial correction method for elastic stresses and strains at notches. The correction scheme, which is numerically cheap, is based on Jiang's model of elastoplasticity. Both mathematical stress-strain computations (nonlinear PDE with Jiang's constitutive material law) and physical strain measurements have been approximized. The gradient evaluation with respect to the parameters, which is large-scale, is realized by the automatic forward differentiation technique.Holger Lang; Rene Pinnau; Klaus Dreßlerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1702Sat, 21 Jan 2006 15:51:35 +0100A multiaxial stress-strain correction scheme
https://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1701
A method to correct the elastic stress tensor at a fixed point of an elastoplastic body, which is subject to exterior loads, is presented and analysed. In contrast to uniaxial corrections (Neuber or ESED), our method takes multiaxial phenomena like ratchetting or cyclic hardening/softening into account by use of Jiang's model. Our numerical algorithm is designed for the case that the scalar load functions are piecewise linear and can be used in connection with critical plane/multiaxial rainflow methods in high cycle fatigue analysis. In addition, a local existence and uniqueness result of Jiang's equations is given.Holger Lang; Rene Pinnau; Klaus Dreßlerreporthttps://kluedo.ub.uni-kl.de/frontdoor/index/index/docId/1701Sat, 21 Jan 2006 15:51:16 +0100